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arXiv:1503.05125 · Applied Physics Letters

Towards a feasible implementation of quantum neural networks using quantum dots

Mikhail V. Altaisky, Nadezhda N. Zolnikova, Natalia E. Kaputkina, Victor A. Krylov, Yu. E. Lozovik, Nikesh S. Dattani

Published Mar 7, 2016• 31 citations
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Abstract

We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations, which are based on SQUID-based systems operating at temperatures in the mK range.

DOI
10.1063/1.4943622

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We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations, which are based on SQUID-based systems operating at temperatures in the mK range.
We present the results of the simulation of a quantum neural network based on quantum dots using numerical method of path integral calculation.In the proposed implementation of the quantum neural network using an array of single-electron quantum dots with dipole-dipole interaction, the coherence is shown to survive up to 0.1 nanosecond in time and up to the liquid nitrogen temperature of 77K.We study the quantum correlations between the quantum dots by means of calculation of the entanglement of formation in a pair of quantum dots on the GaAs based substrate with dot size of 10 0 ÷ 10 1 nanometer and interdot distance of 10 1 ÷ 10 2 nanometers order.
Abstract We present the results of simulation of the dynamics of a 3 quantum dot array by means of numerical solution of the von Neumann equation ıρ˙=[H,ρ].\imath \dot {\rho } = [H,\rho ].ρ˙​=[H,ρ]. The trace over the states of phonon bath was taken by Feynman path integral numerical calculation. It is shown that simplistic system of 3 quantum dots with common phonon bath can implement ¬\neg ¬XOR logic operation. The results of our model can be applied to the development of different quantum simulators, quantum gates, and quantum neural networks implemented in arrays of quantum dots.
The idea of quantum artificial neural networks, first formulated in [34], unites the artificial neural network concept with the quantum computation paradigm. Quantum artificial neural networks were first systematically considered in the PhD thesis by T. Menneer (1998). Based on the works of Menneer and Narayanan [42, 43], Kouda, Matsui, and Nishimura [35, 36], Altaisky [2, 68], Zhou [67], and others, quantum-inspired learning algorithms for neural networks were developed, and are now used in various training programs and computer games [29, 30]. The first practically realizable scaled hardware-implemented model of the quantum artificial neural network is obtained by D-Wave Systems, Inc. [33]. It is a quantum Hopfield network implemented on the basis of superconducting quantum interference devices (SQUIDs). In this work we analyze possibilities and underlying principles of an alternative way to implement quantum neural networks on the basis of quantum dots. A possibility of using quantum neural network algorithms in automated control systems, associative memory devices, and in modeling biological and social networks is examined.
We take another step towards the construction of a bench model of quantum neural network hardware: the simulation of a spatial array of quantum dot molecules, acting as a neural network. Like our previous temporal model (1998), this net has none of the "wiring problems" of hardware for traditional neural nets: the necessary connections are supplied by the physical system itself. Computation is performed by the intrinsic physics of the system. The long range character of the phononic interactions takes the net beyond traditional nearest neighbor connectionist systems. Moreover, unlike our temporal model, there would seem to be few inherent problems to the hardware implementation of this architecture.
Quantum reservoir computing is a promising approach for quantum neural networks, capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits suffer from limited connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits: with just two coupled quantum oscillators, we create a quantum reservoir comprising up to 81 neurons. We obtain state-of-the-art accuracy of 99 % on benchmark tasks that otherwise require at least 24 classical oscillators to be solved. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computing, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures, with billions of neurons implemented with only 10 coupled quantum oscillators.
Quantum reservoir computing is a promising approach to quantum neural networks capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits are limited by low connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computation, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures.